Thanks, but that doesn't work. I've checked and unchecked the "Background Processing" checkbox. Although I can't replicate the step I took, I think it was that when the tool finished processing in Foreground, the dialog box shows the messages printed out during the process, and a button in the upper right said something like "Close the Dialog box". Also, somewhere on the dialog box, there was a checkbox (I think) that said "Always close dialog box when tool is finished". That is the checkbox that I enabled and the dialog box ALWAYS closes now.
I guess an ultimate solution is to uninstall ArcMap and re-install so that all the defaults are back to normal...
Jon Mulder